A time frequency analysis of wave packet fractional revivals

We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.Comment: 9 pages, 4 figure

Identifying wave packet fractional revivals by means of information entropy

Wave packet fractional revivals is a relevant feature in the long time scale evolution of a wide range of physical systems, including atoms, molecules and nonlinear systems. We show that the sum of information entropies in both position and momentum conjugate spaces is an indicator of fractional revivals by analyzing three different model systems: $(i)$ the infinite square well, $(ii)$ a particle bouncing vertically against a wall in a gravitational field, and $(iii)$ the vibrational dynamics of hydrogen iodide molecules. This description in terms of information entropies complements the usual one in terms of the autocorrelation function

Edge-Magnetoplasmon Wave-Packet Revivals in the Quantum Hall Effect

The quantum Hall effect is necessarily accompanied by low-energy excitations localized at the edge of a two-dimensional electron system. For the case of electrons interacting via the long-range Coulomb interaction, these excitations are edge magnetoplasmons. We address the time evolution of localized edge-magnetoplasmon wave packets. On short times the wave packets move along the edge with classical E cross B drift. We show that on longer times the wave packets can have properties similar to those of the Rydberg wave packets that are produced in atoms using short-pulsed lasers. In particular, we show that edge-magnetoplasmon wave packets can exhibit periodic revivals in which a dispersed wave packet reassembles into a localized one. We propose the study of edge-magnetoplasmon wave packets as a tool to investigate dynamical properties of integer and fractional quantum-Hall edges. Various scenarios are discussed for preparing the initial wave packet and for detecting it at a later time. We comment on the importance of magnetoplasmon-phonon coupling and on quantum and thermal fluctuations.Comment: 18 pages, RevTex, 7 figures and 2 tables included, Fig. 5 was originally 3Mbyte and had to be bitmapped for submission to archive; in the process it acquired distracting artifacts, to upload the better version, see http://physics.indiana.edu/~uli/publ/projects.htm